Abstract Non-linear regression is a fundamental and yet under-developing methodology in solving many problems in Artificial Intelligence. The canonical control and predictions mostly utilize linear models or multi-linear models. However, due to the high non-linearity of the systems, those linear prediction models cannot fully cover the complexity of the problems. In this paper, we propose a robust two-stage hierarchical regression approach, to solve a popular Human-Computer Interaction, the unconstrained face-in-the-wild keypoint detection problem for computers. The environment is the still images, videos and live camera streams from machine vision. We firstly propose a holistic regression model to initialize the face fiducial points under different head pose assumptions. Second, to reduce local shape variance, a hierarchical part-based regression method is further proposed to refine the global regression output. Experiments on several challenging faces-in-the-wild datasets demonstrate the consistently better accuracy of our method, when compared to the state-of-the-art.